A few minutes of idle googling has not uncovered a route. I know that the ancient vikings used to travel from the Baltic to the Black sea by portaging, but I’m curious as to whether or not a viable canal was ever built, and if so, is it still in operation? Boatnerd.com, my favorite site for all things boatlike locally, is of no help.
You can take the Elbe-Lübeck Canal from Lübeck to Lauenberg, the Elbe Seiten Canal to Wolfsburg, the Mittel-Land Canal to Osnabruck, the Hase to the Rhine at Duisberg, the Rhine to the Main at Wiesbaden, the Main to the Rhine-Main-Danube canal at Bamburg, the Canal to the Danube at Kelheim, and the Danube the rest of the way to the Black Sea.
Cool! Thanks, Prince of Cats!
The route is a bit roundabout, but as it says in the Books of Bokonon, “Unusual travel suggestions are dancing lessons from God”.
No problem. 
A minor correction, I’m afraid - don’t take the Mittlel-Land Canal to Osnabruck, stay on it until you get to Hörstel, then take the Dortmund-Ems Canal to Datteln and the Rhine-Herne Canal to join the Rhine at Duisberg.
Most info obtained from http://de.wikipedia.org .
That looks like a fun trip if one had the time, but I’d have thought that the Volga-Baltic Waterway in conjunction with the Volga-Don Canal was more direct.
Russian inland cruises.